If you have to reduce price of a product without a new replacement product in the market then that is a sign of trouble with business growth rather than a strategy. It goes down hill from there. Only few companies have managed to do this successfully and that too if they rely on commodity BoM whose prices go down or if their service does not require frequent changes/upgrade once developed.
One trick I learnt from a presentation few years ago was to set appropriate price for a product such that you don't make a loss, but give(for a fixed duration) a 100%(or whatever you decide) discount on that price for early customers. That way the customers know what the actual price of that product is and they are also aware that the discount is a fixed time offer. Now you have three levers to play with: the actual product price, the discount and the duration of the offer.
Another trick is to set the correct price for the product, but give some freebies along with the product to get customers on board. The freebies are one-time or for limited period.
This is a strategy used by auto makers for ages, the same model goes slightly upmarket so that even if you stick with the same model you pay more. Sometimes it a model will fall in price to make room for a new entry in-between. The other way thing that's done is renumbering models so that you're coerced into choosing the one slightly upmarket.
Bonus points if you can quantify what the limited period would be, instead of leaving it vague. This is how most of the good sellers do (be it a SaaS or some other content or service).